The difficulty of constructing de Sitter vacua in string theory (See ref. [1]} for a review) leads to a discrepancy with cosmology. Also, the swampland conjecture [2]}, [3]}, [4]} has revived the debate on how a de Sitter universe, modeling inflation or the Universe dominated by dark energy, can be consistent with string theory. Recently, it was pointed out that an expanding bubble in a five-dimensional anti-de Sitter (AdS) spacetime mimics a four-dimensional de Sitter spacetime on the bubble [5]}, [6]}, [7]}. The idea of the realization of the Universe on a brane was pioneered in Ref. [8]}. The nucleation of an expanding bubble can be realized in a meta-stable AdS\({}_5\)  vacuum via the Coleman de Luccia (CdL) transition [9]}. The nucleated bubble mediates two different AdS\({}_5\)  vacua, and the interior vacuum has a smaller vacuum energy density.
